Problem: Express your answer as a mixed number simplified to lowest terms. $6\dfrac{2}{5}-3\dfrac{5}{9} = {?}$
Solution: Find a common denominator for the fractions: $= {6\dfrac{18}{45}}-{3\dfrac{25}{45}}$ Convert ${6\dfrac{18}{45}}$ to ${5 + \dfrac{45}{45} + \dfrac{18}{45}}$ So the problem becomes: ${5\dfrac{63}{45}}-{3\dfrac{25}{45}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{63}{45}} - {3} - {\dfrac{25}{45}}$ Bring the whole numbers together and the fractions together: $= {5} - {3} + {\dfrac{63}{45}} - {\dfrac{25}{45}}$ Subtract the whole numbers: $=2 + {\dfrac{63}{45}} - {\dfrac{25}{45}}$ Subtract the fractions: $= 2+\dfrac{38}{45}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{38}{45}$